## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{2}{3}$
Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $\log_{1000}100 ,$ is equivalent to \begin{array}{l}\require{cancel} \log_{1000}1000^{2/3} \\\\= \dfrac{2}{3}\log_{1000}1000 .\end{array} Since $\log_bb=1,$ the expression, $\log_{1000}1000 ,$ simplifies to $1$. \begin{array}{l}\require{cancel} \dfrac{2}{3}(1) \\\\= \dfrac{2}{3} .\end{array}